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个人信息Personal Information
教授 博士生导师 硕士生导师
性别：男
毕业院校：山东大学
学历：研究生(博士)毕业
学位：理学博士学位
在职信息：在职
所在单位：数据科学研究院
入职时间：2019-08-30
学科：基础数学
办公地点：明德楼C701
联系方式：(0531) 883 69786
L-functions
Spring 2022, Jinan
Time and Place:
Tuesday 14:00-15:50, Mingde Building C704.
Prerequisites:
Basic Analytic Number Theory and Modular Forms.
Syllabus:
This is a reading course. We plan to read the following papers in this semester.
[S21]. Soundararajan, K. The distribution of values of zeta and L-functions. ArXiv preprint, arXiv:2112.03389, 2021.
[RS05]. Rudnick, Z.; Soundararajan, K. Lower bounds for moments of L-functions. Proc. Natl. Acad. Sci. USA 102 (2005), no. 19, 6837–6838.
[S09]. Soundararajan, K. Moments of the Riemann zeta function. Ann. of Math. (2) 170 (2009), no. 2, 981–993.
[S08]. Soundararajan, K. Extreme values of zeta and L-functions. Math. Ann. 342 (2008), no. 2, 467–486.
[RS15]. Radziwiłł, M.; Soundararajan, K. Moments and distribution of central L-values of quadratic twists of elliptic curves. Invent. Math. 202 (2015), no. 3, 1029–1068.
Schedule:
| Date | Speaker | Title | References |
| February 22 | Bingrong Huang | Moments of L-functions (Lower bounds) | [RS05] |
| March 1 | Shenghao Hua | Values at the edge of the critical strip | [S21] §1 |
| March 8 | Shenghao Hua | Selberg's central limit theorem | [S21] §2 |
| March 15 | Yuxuan Zhou | Selberg's theorem in families of L-functions | [S21] §3 |
| March 22 | Hui Wang | Moments of L-functions | [S21] §4 & [S09] |
| March 29 | Mingyue Fan | Conjectures of moments | [S21] §5 |
| April 5 | no talk (Qing Ming) | ||
| April 12 | Mingyue Fan | Conjectures of moments | [S21] §5 |
| April 19 | Tengyou Zhu | Results on moments and FHK conjecture | [S21] §6 |
| April 26 | Tengyou Zhu | Results on moments and FHK conjecture | [S21] §8 |
| May 03 | Enxun Huang | Extreme values | [S21] §7 |
| May 10 | Enxun Huang | Extreme values | [S08] |
| May 17 | Sizhe Xie | [RS15] | |
| May 24 | Sizhe Xie | [RS15] | |
| May 31 | Liangxun Li | [RS15] | |
| June 07 | Liangxun Li | [RS15] | |
| June 14 | Mingyue Fan | [RS15] | |
Contact: Bingrong Huang (Email: brhuang@sdu.edu.cn; Office: Mingde Building C701)
Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1454369/list/index.htm